The derivative of a function f is given by f′(x)=0.1x+e0.25x . At what value of x for x>0 does the line tangent to the graph of f at x have slope 2 ?

Question

I have homework in AP calculus

Answer 1

The derivative is 0.1+.25e^.25x and it must = 2

1.9/.25=e^.25x

ln(1.9/.25) = .25x

x = (1/.25)ln(1.9/.25)

I will leave the arithmetic to you.